Regularization by noise for stochastic Hamilton-Jacobi equations
- Authors: Paul Gassiat, Benjamin Gess
- Preprint year: 2016
- First public date: 2016-09-22
- arXiv: 1609.07074
- Status: Published
- Publication type: Journal article
- Publication year: 2019
- Journal: Probability theory and related fields, 173 (2019) 3/4, pp. 1063-1098
- DOI: 10.1007/s00440-018-0848-7
Abstract
We study regularizing effects of nonlinear stochastic perturbations for fully nonlinear PDE. More precisely, path-by-path $L^{\infty}$ bounds for the second derivative of solutions to such PDE are shown. These bounds are expressed as solutions to reflected SDE and are shown to be optimal.